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Well Posedness

Well Posedness

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Publisher:

Princeton University Press

DOI:10.23943/princeton/9780691142173.003.0012

This chapter first presents a model for the Maxwell equations for complex random media in terms of stochastic integrodifferential equations. It then provides the appropriate functional framework that can allow for the treatment of the problem as an abstract stochastic integrodifferential equation in Hilbert space. In exploiting this framework, the chapter provides some solvability and well-posedness results for this model, using a semigroup-based approach. Hereafter, this chapter proposes alternative approaches to solvability and well posedness for the stochastic integrodifferential equations that arise in the modelling of random complex electromagnetic media, using either the finite-dimensional approximation (Faedo-Galerkin method) or the Wiener chaos approach.

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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see www.princeton.universitypressscholarship.com/page/privacy-policy).date: 19 November 2018